Critical discussion of simple adsorption methods used to evaluate the micropore size distribution

The well-known simple adsorption methods used to evaluate the micropore size distribution from low pressure adsorption isotherms were examined by employing model isotherms for slit-like graphite micropores obtained from nonlocal density functional theory. It was shown that in the range of pore sizes from about 0.4 to 0.9 nm, the Horvath Kawazoe (HK) method satisfactorily reproduces the shape of the micropore size distribution, but the pore sizes are underestimated. In the case of micropores wider than 0.9 nm, the method fails as the formation of the monolayer on the pore walls produces a peak corresponding to 0.6 nm micropores on the HK pore size distribution. Therefore, the HK method indicates the presence of microporosity even for nonporous samples. The Dubinin-Astakhov adsorption isotherms were also examined and it was shown that their application to represent local adsorption isotherms for homogeneous pores is questionable. However, the adsorption potential distributions seem to be promising for micropore analysis.Nomenclature A Adsorption potential kJ/mol - C ₁ Constant in Eq. 3 and 4 kJ * nm/mol - C ₂ Constant in Eq. 3 and 4 nm³ - C ₃ Constant in Eq. 3 and 4 nm⁹ - C ₄ Constant in Eq. 3 and 4 - d Adsorbate molecule diameter nm - d _A Adsorbent atom diameter nm - G Change in the Gibbs free energy kJ/mol - J Pore size distribution cm³/(g*nm) - R The universal gas constant = 8.31431 J/(mol * K) - T Absolute temperature K - V Amount adsorbed expressed in cm³ of liquid adsorbate per 1 g of the adsorbent = 0.0015468 * amount adsorbed expressed in cm³ STP/g cm³/g - x Pore width nm - X Differential adsorption potential distribution cm³ * mol/(g*kJ) - Constant defined as nm - p Pressure Pa - p ₀ Saturated pressure = 760 torr = 101325 Pa Pa - P _c Condensation pressure Pa - Degree of pore filling - S _BET BET specific surface area m²/g - S _ex External surface area obtained fromt-plot method m²/g - V _mi Micropore volume obtained fromt-plot method cm³/g - V ₁ Total pore volume cm³/g - E Characteristic energy in the Dubinin-Astakhov equation kJ/mol - n Exponent in the Dubinin-Astakhov equation      

Approximate upper bounds to the momentum expectation value ratios 〈p 2〉/〈p −1〉 and 〈p〉/〈p −1〉 in atoms

Within an isoelectronic series of atoms, reasonably tight upper bounds on the ratios of the momentum expectation values ;p ²/;p ^–1 and p/p ^–1 respectively have been derived for the first time by using the Dresher's inequality.     

Excited state wave functions

Wave functions and energies were calculated for the 2s, 3p ₀, and 4d ₀ states of the hydrogen atom using the Messmer and Rayleigh-Ritz variational methods with minimization of the second eigenvalue. The wave functions were linear expansions of Gaussian functions and both linear and exponential parameters were varied. Except for the two term expansions, calculated values of the energies and expectation values, r ^–1, r and r ² were within two percent of the true values for both methods.     

Texture of Electrolytic Platinum Deposited on Polycrystalline Gold

Platinum deposits of submicron thicknesses on polycrystalline gold substrates subjected to different thermal treatments and characterized by texture 200, 311, and 220 are characterized by methods of x-ray diffractometry and scanning electron microscopy. No deposits prepared in a potentiostatic mode exhibit a pronounced texture or a reliable correlation between a weak texture of a deposit and the substrate texture. Established is the difference of predominant directions of secondary nucleation–growth of deposit on neighboring grains of the substrate. The assumption that the deposit includes fragments the size of a few tens of micrometers with pronounced texture of different directions is substantiated.     

Average electron momenta in many-electron atoms

In many-electron atoms, the average electron momentum p represents the mean momentum of a single electron when all the electron motions are averaged. If any two electrons are considered simultaneously, however, the average momentum p splits into two different momenta, low momentum p_< and high momentum p_>. For the 102 atoms He through Lr in their ground states, the momenta p_< and p_> are systematically examined at the Hartree–Fock limit level. It is also shown that the sum p_>+p_< and the difference p_>–p_< of the two momenta constitute upper and lower bounds to the electron-pair relative momentum p₁₂=|p₁–p₂| and to the electron-pair center-of-mass momentum P=|p₁+p₂|/2. The tightness of the bounds is discussed for the 102 atoms.     

Microwave Spectrum and Dipole Moment of 1,3‐dioxolane in the Hindered‐Pseudorotation States v = 0, 1, 2, and 3

The microwave spectrum of 1,3dioxolane (C₃H₆O₂) in the ground and first three excited states of hindered pseudorotation was studied. The transitions corresponding to the _b, _c, and _a components of the dipole moment were identified. The spectrum was analyzed using numerical diagonalization of the effective rotational Hamiltonian for four interacting states of hindered pseudorotation. The rotational constants, centrifugal distortion constants, the constants of interaction between general rotation and hindered pseudorotation, and the distances between the quasidegenerate vibrational levels ₀₁ = 64840.5, ₁₂ = 122231.7 and ₂₃ = 119732.7 MHz are determined. From the Stark effect of microwave transitions, the dipole moment components (in Debye units) in the hinderedpseudorotation states v = 0, 1, 2, and 3 are determined: 0|_b|0 = 1|_b|1 = 1.22, 2|_b|2 = 1.20, 3|_b|3 = 1.21, 0|_c|1 = 0.77, 2|_c3 = 0.66, and 1|_a|2 = 0.19.     

Moment Scaling at the Sol-Gel Transition

Two standard models of sol-gel transition are revisited here from the point of view of their fluctuations in various moments of both the mass-distribution and the gel-mass. Bond-percolation model is an at-equilibrium system and undergoes a static second-order phase transition, while Monte-Carlo Smoluchowski model is an off-equilibrium one and shows a dynamical critical phenomenon. We show that the macroscopic quantities can be splitted into the three classes with different scaling properties of their fluctuations, depending on whether they correspond to: (i) noncritical quantities, (ii) critical quantities or to (iii) an order parameter. All these three scaling properties correspond to a single form: M P(M) = ((M – M)/ M), with the values of respectively: = 1/2 (regime (i)), 1/2 and 1 (regime (ii)), and = 1 (regime (iii)). These new scalings are very robust and, in particular, they do not depend on the precise form of an Hamiltonian.     

Two-electron atomic wave functions which satisfy proportionality relations between one-and two-electron moments

Based on momentum- and position-space analyses of the moment operators for two-electron atoms, it is shown that there exists a family of two-electron wave functions which satisfy a proportionality relation, r/ ₁ ^v /r ₁₂ ^v =p/ ₁ ^v /p ₁₂ ^v =2^–v/2, between the one and two-electron moments in position and momentum spaces, where v is an arbitrary number for which the moments are well-defined.     

Coordination of Heterovalent Iron Atoms in SrCo1 – yFeyO3 – zSolid Solutions

Mössbauer spectroscopy was used to study hyperfine interactions on ⁵⁷Fe nuclei of SrCo_{1 – y} Fe _y O_{3 – z} solid solutions (0.2 y 0.8). The ⁵⁷Fe spectra measured in the paramagnetic temperature range look like a superposition of two quadrupole doublets whose parameters correspond to high-spin Fe⁴⁺cations ( = 0.1 mm/s; = 0.4 mm/s) in the anion surrounding with coordination number 5 (tetragonal pyramid) and to Fe³⁺cations ( = 0.3 mm/s; = 0.4 mm/s) in the distorted octahedral environment. The relative number and pattern of distribution of heterovalent cations (Co⁴⁺, Co³⁺, Fe⁴⁺, and Fe³⁺) in the B-sublattice of perovskites were determined. The values of the electronic exchange constants in the solid solutions obtained through Mössbauer spectroscopy were compared with those obtained from thermodynamic calculations. The oxygen penetration in perovskites was found to depend on their composition and structure.     

Fonctions autocohérentes et intégrales radiales pour les ions de la série du fer

The radial integrals 3d¦r ^k ¦3d, k=–3, –1, 2, 4 and 4p¦r ^k ¦3d, k= 1, 3 for first-row transition-metal ions have been computed from analytical self-consistent field wave functions. The expressions 4p¦r ^k ¦3d allow to compute the oscillator strengths of dipolar electric transitions for an trapped in a crystalline matrix iron group ion. Les intégrales 3d¦r ^k ¦3d, k=–3, –1, 2, 4 et 4p¦r ^k ¦3d, k=1, 3, relatives aux ions de la première série de transition, sont calculées à l'aide de fonctions radiales _3d et _4p , autocohérentes. Les expressions 4p¦r ^k ¦3d permettent d'évaluer les forces d'oscillateur de transitions dipolaires électriques relatives à un ion du groupe du fer engagé dans une matrice cristalline.     

Zur Totalsynthese von Human-Sekretin

Summary The synthesis of the heptacosapeptide amide with the primary structure of Human-secretin is described. For this purpose 7 fragments were designed, i.e. H-Gly-Leu-Val-NH₂ 25–27b,Z-Arg(Z ₂)-Leu-Leu-Gln-OH 21–24,Z-Arg(Z ₂)-Leu-Gln-OH 18–20,Z-Arg(Z ₂)-Glu(OtBu)-Gly-Ala-OH 14–17,Z-Arg(Z ₂)-Leu-OH 12–13,Z-Thr(tBu)-Ser(tBu)-Glu(OtBu)-Leu-Ser(tBu)-OH 7–11,Adoc-His(Adoc)-Ser(tBu)-Asp(OtBu)-Gly-Thr(tBu)-Phe-OH 1–6 these fragments were consequently assembled to the overall protected total sequence using the Wünsch/Weygand-method with dicyclohexylcarbodiimide. After deprotection by exposure to trifluoroacetic acid in presence of 1,2-ethanedithiol and water as scavenger, the isolated crude product was purified by column chromatography on CM-Sepharose, fast flow. This synthetized Human-secretin showed the full biological activity in comparison to Porcine-secretin.

Herrn Prof. Dr. E. Bayer zum 65. Geburtstag gewidmet.     

On a variational method for determining excited state wave functions

A variational method is proposed which results in an approximate wave function for an excited state which has the maximum overlap with the true excited state eigenfunction. The method involves the calculation of the quantities E=¦H¦ and =¦(H-E)²¦, but is free of the constraint that the trial function must remain orthogonal to all states of the same symmetry which lie beneath it. One must know, however, an approximation to the true eigenvalue. A discussion is given on how one might gain the latter information, lacking knowledge of the spectrum, from the repeated application of the method.

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Zusammenfassung Es wird eine Variationsmethode vorgeschlagen, die auf eins genäherte Wellenfunktion für einen angeregten Zustand führt, welche sich maximal mit der wahren Eigenfunktion des angeregten Zustandes überlappt. Die Methode ermöglicht die Berechnung der Größen: E=¦H¦ und =¦(H-E)²¦, ist aber frei von der Nebenbedingung, daß die Versuchsfunktion orthogonal zu allen benachbarten Zuständen mit derselben Symmetrie bleiben muß. — Man will jedoch eine Näherung des wahren Eigenwertes wissen. — Eine Diskussion darüber, wie man durch wiederholte Anwendung der Methode letztere Information gewinnen kann, ohne Kenntnisse über das Spektrum zu besitzen, wird durchgeführt.

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Résumé Méthode variationnelle pour la détermination d'une fonction d'onde d'un état excité présentant le recouvrement maximum avec la fonction d'onde exacte. La méthode implique le calcul de E=¦H¦ et =¦(H-E)²¦ mais ne comporte pas la contrainte d'orthogonalité de la fonction d'essai à tous les états inférieurs de même symétrie. On doit cependant connaître une valeur approchée de la valeur propre exacte. Discussion sur la manière dont on peut obtenir cette valeur approchée sans connaître le spectre, par application répétée de la méthode.

     

Upper bounds to atomic electron densities in position and momentum spaces

Modified functions r ^–(r) and p ^–(p) of the spherically averaged electron densities (r) in position space and (p) in momentum space are found to be convex (i.e., the second derivatives are nonnegative everywhere) for all the 103 ground-state atoms from hydrogen (atomic number Z=1) to lawrencium (Z=103), if the parameters are chosen to be 0.6 and 1.4. The convex property of r ^–(r) and p ^–(p) is used to derive upper bounds to the density functions (r) and (p) in terms of their radial moments r ^s and p ^s or frequency moments ^t and ^t . In most cases, the present bounds are shown to be more general and more accurate than those reported in the literature.     

Comparison of the crystal structures of Co2(X 2O7)·2H2O,X=P and As

Summary Crystals of Co₂(X ₂O₇)·2H₂O,X=P/As were synthesized under hydrothermal conditions. Their crystal structures were determined by single crystal X-ray diffraction:a=6.334(1)/6.531(2),b=13.997(2)/14.206(4),c=7.637(1)/7.615(2)Å, =94.77(2)/94.74(2)°, space group P2₁/n,R=0.032/0.046,R _w=0.028/0.034 for 2423/2042 reflections and 131/119 variables. Within the twoXO₄ tetrahedra connected via a common corner to anX ₂O₇ group the average P-O bond lengths are approximately equal (1.540 and 1.543 Å), but As-O differs significantly (1.685 and 1.696 Å). A comparison with the isotypic Mn and Mg pyrophosphates shows a correlation between the ratio Me-O/X-O and the angle O-X-O.

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Vergleich der Kristallstrukturen von Co₂(X ₂O₇)·2H₂O,X=P und As

Zusammenfassung Kristalle von Co₂(X ₂O₇)·2H₂O,X=P/As wurden unter Hydrothermalbedingungen synthetisiert. Ihre Kristallstrukturen wurden mittels Röntgenbeugung an Einkristallen bestimmt:a=6.334(1)/6.531(2),b=13.997(2)/14.206(4),c=7.637(1)/7.615(2) Å, =94.77(2)/97.74(2)°, Raumgruppe P2₁/n,R=0.032/0.046,R _w=0.028/0.034 für 2423/2042 Reflexe und 131/119 Variable. In den beiden über eine gemeinsame Ecke zuX ₂O₇-Gruppen verknüpftenXO₄-Tetraedern sind die mittleren P-O-Abstände ungefähr gleich (1.540 und 1.543 Å), hingegen differiert As-O signifikant (1.685 und 1.696 Å). Ein Vergleich mit den isotypen Mn- und Mg-Pyrophosphaten zeigt eine Korrelation zwischen dem Quotienten Me-O/X-O und dem WinkelX-O-X.

     

Vibrational relaxation by collision in polyatomic molecules

A model of a harmonic oscillator with friction is used to discuss the conversion of translational energy to vibrational by collision of an atom with a polyatomic molecule. It is shown that adiabatic conversion implies that E ² may substantially exceed the value calculated, neglecting the interaction of the bond with the rest of the molecule.     

A new flavonoid isolated from the leaves ofCynara scolymus L.

Summary The fresh leaves of the artichokeCynara scolymus L. have yielded a new flavonoid glycoside, cynarotriside, having the structure luteolin 7-[O--D-glucopyranosyl-61-O--L-rhamnopyranoside]-4-O--D-glucopyranoside.Khimiya Prirodnykh Soedinenii, Vol. 2, No. 1, pp. 16–20, 1966     

The restriction of spin contamination in unrestricted Hartree Fock wave functions

A method is developed to study in detail the contaminating spin components in UHF calculations for free radicals. Applications are made to those cases previously reported in which normal parametrisation of PPP UHF calculations lead to values of S ² which increase on annihilation of the contaminating quartet component.

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Zusammenfassung Es wird eine Methode entwickelt, um detaillierte Untersuchungen der bindenden Spinkomponenten in UHF-Rechnungen für freie Radikale zu ermöglichen. Es werden Anwendungen für solche Fälle, über die schon früher einmal berichtet wurde, durchgeführt, bei denen die normale Parametrisierung von PPP-UHF-Rechnungen zu Werten von S ² führte, welche die Vernichtung der bindenden Quartettkomponente anwachsen lassen.

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Résumé Développement d'une méthode pour étudier en détail les composantes de spin étrangères dans les calculs UHF des radicaux libres. On l'applique aux cas précédemment considérés dans lesquels des calculs UHF avec paramétrisation PPP conduisent à des valeurs de S² qui croissent lorsque l'on annule la composante quartet.

     

An alternative way to analyze quasi-elastic light scattering data for broadly distributed samples

In Quasi-Elastic Light Scattering (QELS), an apparent average hydrodynamic radius can be calculated from the measuredz-average translational diffusion coefficient D _z by using the Stokes-Einstein equation: withk _B,T and being the Boltzmann constant, the absolute temperature and the solvent viscosity, respectively. It is known thatR _{h, app} is not the same as R _{h z} because , especially when a sample is broadly distributed. In order to obtain R _{h z} instead ofR _{h, app}, an alternative way to analyze QELS data is proposed: at first, we manipulate the measured correlation functionb ^1/2|g ⁽¹⁾(t)| into a new function ; and then, we can analyze this new function to obtain an apparent parameter D_app and an apparent distribution width . We have shown that no matter how broadly a sample is distributed, D_app can be easily reduced to R _{h z} , and is directly related to the distribution width. In this report, besides using a simulated time correlation function, we also used two measured correlation functions of a latex dispersion with a broad particle size distibution and a polystyrene standard with a broad molecular weight distribution to demonstrate this alternative way.     

Shear-induced deformation of polystyrene coils in dilute solution from small angle neutron scattering 2. Variation of shear gradient,molecular mass and solvent viscosity

The technique of small angle neutron scattering (SANS) has been used to study the conformation of polystyrene chains in dilute solution under a constant shear gradient. The experiments reveal a distinct anisotropy of the molecular dimensions with regard to the directions parallel and perpendicular to the flow direction on the 2D-multidetector. The deformation ratio of the single polymer chain (R ²/R _iso ² )–1 as a function of the reduced shear gradient=([] · · M _w G)/RT shows a transition from the ideal ²-behaviour for dynamic infinitely flexible coils found at small gradients, to a behaviour with smaller increase at larger. These results are qualitatively consistent with the theory of Cerf for a polymer with finite internal viscosity in a shear gradient. At low(<1), a better agreement with the model of a free-draining coil (Rouse behaviour) than with the Zimm model is observed.     

Analysis of correlation effects in HeI,LiI and BeI iso-electronic sequences by Z-expansion methods

Correlation effects for the energy and the expectation values of the electron-nuclear attraction and the inter-electronic repulsion in atomic states are discussed in terms of Z expansions for these quantities. Numerical examples are given for the HeI, LiI and BeI iso-electronic sequences.It is shown that a series expansion of the type V _en =2₀Z² + ₁Z (a.u.) gives very accurate results for the expectation value of the electron-nuclear attraction.

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Zusammenfassung Der Korrelationsanteil an der Energie und an den Erwartungswerten der Elektron-Kernanziehung sowie der Elektronenabstoßung für atomare Zustände wird mit Hilfe der Z-Entwicklung dieser Größen diskutiert. Für die isoelektronischen Reihen HeI LiI und BeI werden numerische Beispiele angegeben. Es wird gezeigt, daß eine Reihenentwicklung vom Typ V _en +2Z² + ₁Z(a.E.) sehr genaue Ergebnisse für den Erwartungswert der Elektron-Kernanziehung liefert.